LetW=(W1,…,Wn) be a random vector of n independent random variables, and let R=(R1,…,Rn) be another random vector having the permutation distribution on {1,2,…,n}, independent of W. If the Wi's are ordered in the likelihood ratio order [resp. the hazard rate order, the reversed hazard rate order, and the usual stochastic order], it is shown that (WR1, WR2,…,WRn) is negatively regression dependent [resp. negatively right tail dependent, negatively left tail dependent, and negatively associated]. Several applications of the main results are also given.